Three-dimensional localization of spins in diamond using ¹²C implantation

The single spin associated with the nitrogen-vacancy (NV) center in diamond provides an advantageous platform for spin-based quantum science and technology. The NV center's long spin coherence time (T₂) at room temperature¹ and the inherent atomic scale of the defect enable nanometer-scale magnetometry applications including single electron spin imaging^2,3 and external nuclear spin sensing.^4–6 In addition, the optical addressability of NV center spins provides a spin-light interface for quantum communications^7,8 leading to schemes of photon-mediated spin coupling.^9,10 These NV center properties can be further exploited through nanoscale engineering of the diamond. For example, fabricating the diamond into scanning probe devices for sensing,¹¹ as well as plasmonic cavities¹² and photonic crystals,^13,14 can greatly enhance spatial resolution and photon collection efficiency. Shrinking mechanical structures containing NV centers to the nanoscale could also enable coherent strain-mediated spin interactions.¹⁵ 

A critical challenge to enabling scalable creation of NV-integrated nanostructures is to maintain spin coherence of an NV center localized at a deterministic position with nanoscale precision. Our approach utilizes a nitrogen delta-doping diamond growth technique which forms NV centers with consistently long spin coherence times,¹⁶ while constraining the NV centers in the depth direction. In addition, we use a post-growth vacancy creation process to control NV centers' lateral position for full three-dimensional (3D) localization. In this Letter, we demonstrate a method of vacancy engineering that allows for the tunability and localization of the NV density.

The previous approach to vacancy creation in delta-doped films was via electron irradiation.¹⁶ A drawback to this method is that vacancies are formed throughout the entire grown film and substrate. These non-localized vacancies result in a low density of doped NV centers on the order of 10¹²–10¹³cm⁻³, which limits device integration of these engineered NV centers. Moreover, the significant amount of nitrogen in the substrate prohibits simply increasing the irradiation dose to increase doped NV density, as it would yield more background NV centers contained within the substrate. Since substitutional nitrogen (P1 centers) are a major source of spin decoherence for NV centers,¹⁷ the NV density must be increased without increasing the number of nitrogen atoms incorporated within the diamond crystal. This requirement necessitates vacancy engineering that aims to enhance the conversion efficiency of nitrogen atoms within the delta-doped layer to NV centers.

Here, we report a ¹²C implantation technique that enhances NV density without increasing the amount of doped nitrogen. ¹²C ions are implanted shallower (<∼8 nm) than the nitrogen delta-doped layer (51 nm below the surface) to create a localized layer of vacancies whose depth is controlled via implantation energy. Subsequent annealing diffuses these vacancies into the nitrogen delta-doped layer forming NV centers. As ¹²C has no nuclear spin, NV coherence times will not be limited by a nuclear spin bath.^1,18 We show that the doped NV density can be controlled primarily through the ¹²C implantation dose, and furthermore that this technique can be utilized with aperture implantation¹⁹ to provide 3D localization of single NV centers in a volume of (∼180 nm)³ while still repeatedly preserving long spin coherence times T₂ > 300 μs.

Samples used in this study were grown using a nitrogen delta-doping technique in a diamond plasma-enhanced chemical vapor deposition system. The crystal growth conditions were: a temperature of 800 °C, pressure of 25 Torr, microwave power of 750 W, H₂ flow of 400 sccm, and ¹²CH₄ (>99.998%) flow of 0.1 sccm along with a doping ¹⁵N₂ gas flow in a range of 0.1–10 sccm.¹⁶ We first grew a ¹²C buffer layer (51 or 103 nm thick) on top of a commercially available, electronic grade (100) diamond substrate from Element 6, followed by a 6 nm-thick ¹⁵N delta-doped layer and a ¹²C cap layer (51 nm). The thickness of each layer was estimated by our calibrated growth rate.¹⁶ We doped with isotopically purified ¹⁵N₂ gas (>98%) to differentiate doped ¹⁵NV centers from ¹⁴NV centers in the substrate. After growth, the samples were implanted with ¹²C ions at an implantation energy of 2 or 7 keV. According to our SRIM calculations,²⁰ these implantation energies create vacancies 2.4 ± 2.2 or 8.0 ± 6.1 nm from the surface, respectively (see Figure 1(a)). Creating localized vacancies shallower than the nitrogen delta-doped layer is important to preserve spin coherence of doped NV centers, as the delta-doped layer is deep enough to be protected from crystal damage due to the ion impact. The vacancy layer, however, is still close enough to the nitrogen delta-doped layer that vacancies can diffuse during the subsequent annealing process, creating NV centers in the delta-doped layer. A range of ¹²C implantation doses (10⁹–10¹³cm⁻²) was selected depending on the experiment. After the implantation, the samples were annealed in a H₂/Ar forming gas atmosphere, followed by a surface cleaning process using a perchloric acid mixture.^16,21,22 The sample preparation process and ¹²C implantation technique are summarized schematically in Fig. 1(a). All measurements were performed using a home-built confocal microscopy setup with 532 nm laser excitation at ambient conditions.

First, we demonstrate that the NV centers in the nitrogen delta-doped layer are formed through a vacancy diffusion process. Figure 1(b) shows three confocal photoluminescence (PL) scans at the diamond surface as-implanted (left), after annealing at 800 °C for 30 min (center) and 1 h (right). We used the same sample for this cumulative annealing study and imaged three randomly selected areas on the surface for each annealing step to count the number of formed NV centers. We used continuous-wave electron spin resonance (CW-ESR) measurements to identify the isotopic signature for doped ¹⁵NV centers (circled in red) and substrate ¹⁴NV centers (black).¹⁶ The as-implanted surface showed no trace of NV centers, whereas after 30 min of annealing, we observed that >90% of all investigated NV centers were doped NV centers. When we further annealed for a total of 1 h, we observed both doped (∼70% of measured NV centers) and substrate NV centers. These results are consistent with a picture in which the vacancies diffuse away from the implantation region, pass through the delta-doped layer activating doped NV centers, and ultimately diffuse deeper in the crystal activating substrate NV centers. We note, however, that a quantitative understanding of the vacancy diffusion mechanism is necessary in order to form a procedure that exclusively activates doped NV centers. We also note that in other samples we were able to activate NV centers in a ∼12 nm deep nitrogen delta-doped layer with an implantation energy of 2 keV.²³ 

Next, we investigate how process parameters affect the doped NV density. We grew two samples of nominally identical structure with two different ¹⁵N₂ doping gas flow (10 sccm and 0.1 sccm). The samples were then implanted at 7 keV on three different quadrants with different ¹²C doses (10⁹, 10¹⁰, and 10¹¹cm⁻²), followed by annealing at 850 °C for 30 min. The six figures shown in Fig. 2(a) are surface confocal scans of each quadrant. We identified doped NV centers (circled in red) through their CW-ESR hyperfine signature. We measured three random regions within each quadrant on both samples to build up statistics and calculated the doped NV density by computing the average number of doped NV centers found over the scanned area (10 μm × 10 μm) assuming a 6 nm thickness of the nitrogen doped layer. The numbers at the top left of each figure denote the doped NV density in units of 10¹³cm⁻³. For both ¹⁵N₂ flows, the doped NV density increased from ∼0.1 to ∼1 × 10¹³cm⁻³ when we increased the ¹²C dose from 10⁹ to 10¹⁰cm⁻², suggesting that the doped NV density can be controlled via ¹²C dose. According to secondary ion mass spectrometry (SIMS) measurements,¹⁶ the nitrogen dopant concentration should be (0.8 ± 0.6) × 10¹⁶cm⁻³ for the 10 sccm ¹⁵N₂ flow, which is consistent with the nitrogen spin bath density extracted from NV coherence times in similar films.²⁴ We calculate the nitrogen to NV conversion efficiency ([NV]/[N]), where [NV] is the measured doped NV density and [N] is the estimated nitrogen dopant concentration; the results for the 10 sccm ¹⁵N₂ flow sample are 0.02% and 0.16% for 10⁹ and 10¹⁰cm^{−2 12}C doses, respectively. These low conversion efficiencies suggest that NV center creation is vacancy-limited for these implantation dose regimes. For the 10¹¹cm^{−2 12}C dose cases, the NV density was too high to isolate single doped NV centers, but the integrated PL over the scanned areas increased relative to the 10¹⁰cm⁻² areas suggesting that doped NV density continues to increase with ¹²C dose.²⁵ On the other hand, the doped NV density did not show noticeable ¹⁵N₂ flow dependence in the 10⁹ and 10¹⁰cm⁻² dose areas, even though it was varied over two orders of magnitude, suggesting that the nitrogen incorporation is limited in this regime and has already saturated, and hence weakly controlled by ¹⁵N₂ flow.

We next investigated whether coherence times are affected by the change in vacancy creation density. Figure 2(b) summarizes T₂ results, measured using a Hahn echo sequence, for NV centers created by the ¹²C implantation technique. We measured twenty individual NV centers, five for each of the four combinations of ¹²C doses (10⁹ and 10¹⁰cm⁻²) and ¹⁵N₂ flows (10 and 0.1 sccm). These T₂ times were reproducibly on the order of hundreds of microseconds. In particular, the longest T₂ of a single NV center, (799 ± 77) μs, was measured from the 10⁹cm⁻² dose area of the 0.1 sccm flow sample and is encouragingly comparable to the results from electron irradiated samples.¹⁶ We hypothesize that the outliers showing T₂ < 50 μs are likely caused by local fluctuations in the density of vacancy-related paramagnetic defects that form due to the implantation process and are not fully removed by our annealing procedure.²⁶ 

The means and standard deviations (as error bars) of T₂ over each set of five NV centers are shown in the right panel of Fig. 2(b). The average T₂ time increased from 182 ± 18 (252 ± 93) μs to 235 ± 38 (614 ± 106) μs for 10 (0.1) sccm sample when ¹²C dose is changed from 10¹⁰ to 10⁹cm⁻². A two-way analysis of variance of our complete T₂ data showed a statistically significant main effect for the ¹²C implantation dose (p < 0.05), while the main effect for ¹⁵N₂ flow and the interaction between the two main effects were not statistically significant (p > 0.05).²⁵ There may still be more complicated effects of vacancies and nitrogen affecting the T₂ times, which cannot be deterministically verified from the limited sample set.²⁵ If nitrogen were in fact incorporated proportionately to ¹⁵N₂ flow, we would expect T₂ times to be orders of magnitude different between NV centers in the 0.1 and 10 sccm flow samples.¹⁷ The differences we see in the T₂ times are only within the same order of magnitude between samples, and therefore, the results are consistent with our conclusion from Fig. 2(a) that the nitrogen incorporation is weakly dependent on the doping gas flow.

We further utilize the ¹²C implantation vacancy creation technique to demonstrate 3D position control of NV centers within a nanoscale volume. To achieve a sufficiently high density of NV centers, we increased the nitrogen doped layer thickness and increased the ¹²C dose. We grew a sample containing a 51 nm-thick ¹²C buffer layer, followed by a 51 nm-thick ¹⁵N doped layer and a ¹²C cap layer (also 51 nm). After growth, we patterned an array of apertures of varying diameters (nominally from 50 to 450 nm) on a layer of spin-coated resist (PMMA 950) using an electron beam (EB) lithography technique that masks the rest of the surface area from implantation.¹⁹ The sample was then ¹²C implanted with an increased dose of 10¹³cm⁻² at an implantation energy of 7 keV, and subsequently annealed in H₂/Ar forming gas at 850 °C for 30 min followed by the perchloric acid cleaning. The device process is summarized in Fig. 3(a), and a scanning electron microscope (SEM) image of the patterned apertures is shown in the inset of Fig. 3(b).

In Figure 3(b), we show a surface confocal scan of the processed sample showing patterned PL from NV centers localized by implanting through apertures. The difference in integrated PL of seven columns (A–G, from left to right) reflects the difference in their aperture diameter (larger apertures on the left). In particular, the right two columns (columns F and G) show less PL intensity than other columns since they have smaller diameters. We measured 90 apertures in each column to build up statistics in order to determine how many NV centers are localized per aperture. Figure 3(d) is a histogram showing occurrences of finding n NV centers (n = 0, 1, 2, … 10) per aperture (data shown in blue circles) in column G, which has measured diameter of 114 ± 21 nm. We observed 18% of all measured apertures in this column showing integrated PL consistent with a single NV center. We used a maximum likelihood approach to fit a Poisson distribution (red circles) to these data, which gave a mean value of λ = 0.88 NV centers per aperture.

In order to check validity of our PL-based NV counting method, four of the NV centers showing PL consistent with single NV centers were each tested using photon anti-bunching measurements, including the one circled in red in Fig. 3(b). The result on this NV center is shown in Fig. 3(c), displaying the normalized second order correlation function without background correction at t = 0, g⁽²⁾(0) < 0.5, which confirms we are observing luminescence from a single NV center. We measured the T₂ times of these four single NV centers, again showing a scattering of T₂ times between 60 and 530 μs, reflecting the non-uniform damaging nature of ion implantation. However, we measured an average T₂ of ∼340 μs and two of these displayed long spin coherence times of T₂ ∼ 500 μs, an order of magnitude longer than previously reported T₂ times for position-controlled NV centers using nitrogen implantation technique.¹⁹ The Hahn echo result for the NV center showing the longest T₂ = 530 ± 46 μs is shown in Fig. 3(e).

From these results, we demonstrate that spin coherence can be retained in the three-dimensionally localized single NV centers. The largest uncertainty in the localized volume estimation arises from vacancies diffusing not only in the depth direction, but also delocalizing in the in-plane direction. We estimate the vacancy diffusion length to be $153−67+123$ nm based on our observation that $88+10−18$ % of measured NV centers in the apertures were doped NV centers and assuming a one-dimensional diffusion model.^25,27 If we assume that vacancies diffuse isotropically from the aperture and use the mean value of the estimated vacancy diffusion length, we calculate the localized volume to be 5.7 × 10⁶ nm³, or (179 nm)³, and the corresponding NV conversion efficiency to be 1.9%.²⁵ 

The calculated conversion efficiency is increased only by an order of magnitude from the 10¹⁰cm⁻² (Fig. 2(a)) to 10¹³ cm⁻² (Fig. 3(b)) dose cases. However, the conversion efficiency is affected by the localized volume which sensitively depends on the vacancy diffusion length estimation. Confinement of the NV centers within nanopillars could enable a more precise estimation of the conversion efficiency.²⁵ 

The estimated localized volume is comparable to the length scale of many types of NV-based nanostructures, encouraging integration of these ¹²C-implanted NV centers into devices. For example, photonic crystals fabricated from diamond can have mode volumes of a fraction of (λ / n)³, where λ = 637 nm is the wavelength of the zero phonon line of an NV center, and n = 2.4 is the refractive index of diamond.^13,14 This mode volume makes a monolithic NV-photonic crystal approach viable using our technique, which could lead to the integration of coherent NV centers into photonic network. As another example, proposals for coherent phonon-mediated spin coupling^15,28 require the placement of NV centers close to the surface of nanoscale beams in order to maximize strain induced in the NV centers. Our 3D localization approach is particularly promising for this implementation because of the advantage of nanometer-scale depth control inherent to the nitrogen delta-doping technique.

In summary, we demonstrated a ¹²C implantation technique to control the NV center density in the nitrogen delta-doped layer of a CVD-grown diamond film. Localized vacancies are independently created at a depth shallower than the nitrogen doped layer by tuning the implantation energy and the vacancies subsequently diffuse to activate doped NV centers during the annealing process. These NV centers show long spin coherence times T₂ on par with those of NV centers created via electron irradiation. Furthermore, the NV center density can be controlled with the ¹²C implantation dose. Finally, by using a higher implantation dose through lithographically patterned apertures, we demonstrated that single NV centers can be localized in three-dimensions within a volume of (∼180 nm)³ at a deterministic position while repeatedly retaining their spin coherence times T₂ > 300 μs. Our demonstration of the 3D localization of coherent NV centers is compatible with NV-based nanostructures, enabling scalable creation of spin sensing devices, photonic network of coherent spins, and phonon-mediated spin entanglement. While most potential applications require single NV centers, this technique affords the ability to create dense regions of NV centers which could facilitate quantum registers based on magnetic dipole coupling of proximal spins.^29,30

This work was supported by DARPA and AFOSR. B.A.M. acknowledges support from a Department of Defense (NDSEG) fellowship. B.J.A. acknowledges support from the University of California President's Postdoctoral Fellowship. The authors thank Claire A. McLellan for experimental help, David J. Christle for statistical assistance, and Audrius Alkauskas for useful theoretical discussion.